# Bohn Coefficient Interpretation and Same-Sample Comparison

## Part A: Same-Sample Primary vs Structural Balance Bohn Test

Both regressions estimated on identical sample where both measures are available.

| Variable | Primary Balance | | Structural Balance | |
|:--|--:|--:|--:|--:|
| | Coeff (SE) | p | Coeff (SE) | p |
| debt_lag | 0.0100 (0.0031) | 0.0014 | -0.0056 (0.0030) | 0.0612 |
| output_gap_hp | 0.1215 (0.0160) | 0.0000 | -0.0655 (0.0146) | 0.0000 |
| govt_exp_gap | -0.7386 (0.0188) | 0.0000 | -0.4925 (0.0172) | 0.0000 |
| **N** | 2,216 | | 2,216 | |
| **Countries** | 82 | | 82 | |
| **R²** | 0.213 | | 0.122 | |

## Part B: Bohn β in Debt Dynamics Terms

Estimated β = 0.005 (baseline primary balance Bohn coefficient).

### Primary Balance Response to Debt Level

| Debt/GDP | PB Response (pp GDP) | Interpretation |
|--:|--:|:--|
| 50% | 0.25 | Negligible |
| 75% | 0.38 | Negligible |
| 100% | 0.50 | Weak |
| 150% | 0.75 | Weak |
| 200% | 1.00 | Moderate |
| 300% | 1.50 | Moderate |
| 400% | 2.00 | Moderate |

β ≈ 0.005 implies that a 10pp debt increase yields only 0.05pp primary balance improvement.
This is extremely weak relative to the adjustment required for stabilization.

### Implied Stable Debt Levels (at given r-g)

Autonomous primary balance (constant) ≈ -1.03pp GDP.
Stable debt solves: β × d + pb_auto = (r-g)/100 × d.

| r-g (pp) | Stable Debt/GDP | Note |
|--:|:--|:--|
| 0 | 206% | Stable equilibrium (β > r-g) |
| 1 | No equilibrium | Explosive (β < r-g) |
| 2 | No equilibrium | Explosive (β < r-g) |
| 3 | No equilibrium | Explosive (β < r-g) |

## Key Takeaway

β ≈ 0.005 implies that a 10pp debt increase yields only 0.05pp primary balance improvement — extremely weak relative to the adjustment required for stabilization. At r-g = 0% (as in Japan), debt converges to an equilibrium around 206% of GDP. At r-g ≥ 1%, the Bohn reaction is too weak to offset interest costs, and debt is explosive.